3.6. If F is a field, prove that its only ideals are (0) and F itself.
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Expert's answer
2022-06-19T17:51:56-0400
Let I be an ideal of a field F. Assume that (0)=I and let 0=a∈I. Then as F is a field, there exists a−1∈F such that a−1a=1. Hence 1∈I and I=F. So every non-zero ideal if F is equal to F.
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